Let's say we have a binary compound AB in an enclosed container, and let's say there's a tendency to form B-vacancies so that B atoms/molecules escape and form a vapor. Let's assume there's enough of AB that the pressure saturates before AB$_{1-x}$ decomposes too much. Would the vapor pressure of B be the same as for the pure element B?

  • $\begingroup$ Usually the formation of vacancies is not accompanied by vapor formation. Now, unless the AB compound is in equilibrium with solid B, then, no, the vapor pressure of B over AB will not be the same as B over B. $\endgroup$ – Jon Custer Jan 10 at 18:51
  • $\begingroup$ @JonCuster - for quite a few oxides, for example, gaseous oxygen evolves when oxygen vacancies form, so I wouldn't say that simultaneous vapor and vacancy formation is a rare case $\endgroup$ – voffch Jan 10 at 20:27
  • $\begingroup$ @voffch - indeed, for oxides that is the case (and is exploited by various oxide sensors since the vacancy concentration affects the conductivity). I usually deal more with metal alloys, where losing constituents to the gas phase is not an issue. Your answer below can be applied to the more general case. $\endgroup$ – Jon Custer Jan 10 at 20:30

No. The equilibrium vapor (gas) pressure is defined by the corresponding equilibrium. When it's just the element $\ce{B}$ that evaporates, the equilibrium is $$\ce{B(liquid)<=>B(gas),}$$ and the thermodynamics of evaporation (or sublimation if $\ce{B}$ is solid), such as the Clausius–Clapeyron equation, gives you the equilibrium $p-T$ relationship.

When you have nonstoichiometric compound $\ce{AB_{1-x}}$ which loses $\ce{B}$, the process is quite different. Let's imagine purely hypothetical $\ce{AB}$, in the crystal structure of which neutrally charged $\ce{B}$ vacancies, $\ce{V^x_B}$, can be formed. Then, our hypothetical equilibrium between the gas phase and defects in solid can be written in Kröger–Vink notation as $$\ce{B^x_{B}<=>V^x_{B} + B_{gas}}.$$ In this case, until $\ce{AB_{1-x}}$ decomposes too much, the equilibrium constant $K=\frac{p_B\cdot[\ce{V^x_{B}}]}{[\ce{B^x_{B}}]}$ and its temperature dependence define the "partial pressure of $\ce{B}$ - temperature - composition" relationship for $\ce{AB_{1-x}}$.

Please note that the example above is oversimplified for clarity. In the real-world applications of defect chemistry, point defects in nonstoichiometric solids are often charged, and they tend to interact with each other, complicating the equilibria.


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